MultiInterval Subfactors and Modularityof Representations in Conformal Field Theory
Abstract
We describe the structure of the inclusions of factors ?(E)⊂?(E')' associated with multiintervals E⊂ for a local irreducible net ? of von Neumann algebras on the real line satisfying the split property and Haag duality. In particular, if the net is conformal and the subfactor has finite index, the inclusion associated with two separated intervals is isomorphic to the LongoRehren inclusion, which provides a quantum double construction of the tensor category of superselection sectors of ?. As a consequence, the index of ?(E)⊂?(E')' coincides with the global index associated with all irreducible sectors, the braiding symmetry associated with all sectors is nondegenerate, namely the representations of ? form a modular tensor category, and every sector is a direct sum of sectors with finite dimension. The superselection structure is generated by local data. The same results hold true if conformal invariance is replaced by strong additivity and there exists a modular PCT symmetry.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2001
 DOI:
 10.1007/PL00005565
 arXiv:
 arXiv:math/9903104
 Bibcode:
 2001CMaPh.219..631K
 Keywords:

 Mathematics  Operator Algebras;
 High Energy Physics  Theory;
 Mathematical Physics;
 46L37 (Primary) 81T05;
 46M05 (Secondary)
 EPrint:
 45 pages, AMSLatex 2e. Improvements concerning the exposition. Appendices have been expanded with more details. To appear in Commun. Math. Phys